12 years? Ha! The Homelite my Craftsman replaced was 25 years old! But I was ready for self-propelled.
25 years? Ha! My International Harvester built, with a Kohler engine Cub Cadet is 45 years old! And it is self-propelled - I even get to sit on it and go for a ride. Though, putting on new tires last year cost more than many push mowers cost to buy.
Anyway, OP, for your extremely tiny yard, assuming your square footage estimate is accurate, I agree with the poster above - it's perfect for a reel mower. Wasting money on a self-propelled lawnmower for what amounts to a 20'x25' area is overkill, plus takes up more storage space than a reel mower. You're not going to wear out the lawnmower, so what's more important if you get a gas mower is maintenance. If available, only use 100% gasoline (no ethanol added). If you have to use 10% ethanol, then add the stabil to the gasoline right when you fill your gas jug. After mowing, and the lawnmower has cooled, clean the top and bottom of the mowing deck. Learn which side you have to tilt the lawnmower toward, to avoid problems with oil running out when you're cleaning the bottom. Check the oil level EVERY time you're about to use the lawnmower. Change the oil once annually. Clean the air filter at least annually. The last time you run the mower for the season, run it dry, and learn how to drain the gas out of the float in the carburetor, then attempt to start it several times. Never leave it out in the rain, never cut the grass while it's raining. Do these things, and the mower will last you for decades. Or, keep maintenance to a minimum - get a reel mower; it's ideal for such a small yard.
Incidentally, glancing around the Internet, it seems that less than a 1/4 acre of lawn is considered a small yard. .25 acres is over 10,000 square feet. You sure you're not missing a zero on your 500 square feet?